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During recent online chat with gamers, I asserted that 'go' (and possibly othello) had a larger decision space than chess.

After reading Wikipedia, I realized I failed to account for othello and go 'saturating' the board with pieces and dramatically limiting available moves in the late game.

The opposite is true for chess. The decision space dramatically increases as the board is cleared.

From my non-expert opinion, this phenomenon would shift the balance away from position and towards the individual skill of the expert players. This skill is at the heart of the competition itself. The "precision" of skill would be more relevant in the late game.

So my question is: do master players naively assume the path that brought them to the weaker position is representative of the late game? Does the balance shift away from position enough to warrant the stronger position proving his mettle in late game?

L. Scott Johnson
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I dont know thanks for reading
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    Does the decision tree indeed get larger as pieces get captured? Removing a piece may or may not give other pieces more options of what space to move into, but always eliminates all the options that the removed piece had. Capturing a pawn can open the board up and only eliminate 1 or 2 move options, but capturing a bishop or rook can eliminate up to 14 move options while probably not creating more options than that. I might expect the decision space to increase initially, but then diminish as non-pawns get captured in the mid/late game. – Nuclear Hoagie Feb 10 '22 at 16:42
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    During recent online chat with gamers, I asserted that 'go' (and possibly othello) had a larger decision space than chess. Go? Absolutely. Go is drastically more complex than chess. Othello? Not so much. See https://en.wikipedia.org/wiki/Game_complexity#Complexities_of_some_well-known_games (To summarize, the game tree complexity of Othello/Reversi is 10^58, Chess 10^123, and 19x19 Go a whopping 10^360!) – DJMcMayhem Feb 10 '22 at 17:53
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    @NuclearHoagie In fact, I think this is a major part of what characterizes the phases. In the opening, decision space is rapidly expanding. In the middlegame, it fluctuates as players open close the position. In the endgame, it largely decreases. – Acccumulation Feb 10 '22 at 19:07
  • @Nuclear Hogie #1 my definitions might be technically sloppy. #2 the aspect that i better appreciate is the brute force nature of the end game is effectively irrelevant. The below answers illuminate the difference between possible moves and relevant moves. #3 im not exactly sure how those decision trees ultimately terminate, as i thought you could just chase each other around for infinity... Which is , again technically uninteresting even for me, per the accepted answer. – I dont know thanks for reading Feb 11 '22 at 02:13
  • @djmcmayhem. Yep! Thats literally how this train of thought got started lol, naturally i took the limit as trends towards infinity and evaluated my original assumption. And this forum bridged that gap between irrelevant- to relevant- to elite players. Thanks everyone! – I dont know thanks for reading Feb 11 '22 at 02:19
  • @DJMcMayhem is that 10^360 or 10^360!? Because the latter is insane to comprehend. – Adam Barnes Feb 11 '22 at 16:59
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    @AdamBarnes Haha, even 10^360 is an incomprehensible number. 10^(360!) is beyond the realm of incomprehensibility. The game tree complexity of go is the former :) – DJMcMayhem Feb 11 '22 at 17:01
  • How much have to tried playing any of those games?

    the most obvious part of your exposition seems to be that "for chess… the decision space dramatically increases as the board is cleared."

    Did you notice how much that depends on what pieces are on the board, and in what positions?

    Much more than mere experienced or skilled players, Masters typically don't "naively assume" anything… that's a huge part of what makes them Masters, which applies to chess, go or othello as to cricket, football or tennis.

     – Robbie Goodwin Feb 13 '22 at 19:56
  • Hi @robbie goodwin! Comments are not for extended discussion :) to answer you question, i have only dabbled. I know go is 'large' because its famous for being large. I guessed othello was large, but failed to account for the difference in board size. The real break down was my novice assumption that the end game of chess can last forever, chasing each other around the board for infinity. The forum here articulates how irrelevant that is in practical situation. I dont use 'naive' in the derogatory sense, but in the failed assumption, an infinite space yields possibilities not chased due 2 bored – I dont know thanks for reading Feb 14 '22 at 03:41
  • @robbie goodwin i assume 2 computers playing each other at a master level would never resign. So the odds a hunan player is naive is definitely low, but never zero. Change my mind :) – I dont know thanks for reading Feb 14 '22 at 03:53

3 Answers3

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By the time an expert resigns the decision tree may still be large but its evaluation has become simple. Players usually resign because continuing would be miserable to them and boring to their opponent.

Philip Roe
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    Thanks Philip ! Your first sentence exactly answers my question... Ironically your second sentence is what spawned my question in the first place, as the 2 are superficially unrelated... But i now get how one directly leads to another. Cheers! – I dont know thanks for reading Feb 10 '22 at 12:37
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    An example: Suppose novice has a king and a rook and the move. Grandmaster has a king. There are up to 22 moves possible for the novice, and up to 8 for the grandmaster. After both move, up to about 150 positions can happen. Decision space is therefore still pretty large yet the novice will easily win, no matter grandmaster's skill. Add a queen to the novice, theoretical decision space size is even larger, yet the win is easier. – Zizy Archer Feb 11 '22 at 12:30
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An increase in possible moves does not equate to the number of meaningful choices. If you have ten moves that all win the game, it is not usually hard to pick one. Sometimes endgames are hard because they are obvious.

In Go, even at the end of the game, there is plenty to choose from. At the top level of the game, the exact order of moves may still swindle the result. Not like one move one point better but 1/4th of a point better. It is something that does not matter to me, but to pro-players it does. There are known cases of players resigning after evaluating a loss on half a point.

Joundill
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user2043105
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    Yes, in my very amateurish experience playing Go, it is only in "serious" games that anyone would take the trouble to do the "reading" necessary to (precisely?) judge the points to be gained-or-lost toward the end of the endgame. In less serious games that have not been lopsided, people may not want to invest the energy to ultra-optimize the end-endgame, because almost all the action is over... just play quickly and get done? :) Analogously, it seems that some chess players are not so interested in a friendly end-endgame, and/or are willing to declare an outcome without playing it through. – paul garrett Feb 10 '22 at 20:10
  • @paulgarrett: Apparently, even among 9-dan players there is still a wide variety of playing style, some going largely by intuition and others going largely by exacting counting, such as Lee Chang-Ho. – user21820 Feb 11 '22 at 09:45
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It's quite contrary. Experienced chess players values a fair play and doesn't account on possibilities that opponent will make an error, which will be exploited. So a good chess player would assume that he/she is playing with itself (equally strong player). In this case, usually many game outcomes are determined by difference of captured peaces between you and opponent. Even a difference of one pawn in the beginning can lead to a victory at the end. Of course while board is full, this advantage can quickly be destroyed by opponent later captured peaces. However as board gets more and more empty, situation becomes more unlikely that opponent will reverse captured peaces advantage. So small game fluctuations at the beginning becomes a fatal damage in the end. Like death is a fatal outcome of small entropy accumulations in a lifetime. So by the time experienced chess player sees an unstoppable force, it's wise to resign, not wasting time and energy for a boring game, where is no point to think anymore. And it's not naive, it's a very clever and honored move.

Agnius Vasiliauskas
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    Hi @agnius! Thanks for your answer! This makes perfect sense. I do want to emphasize that im not trying to use 'naive' in derogatory sense. I guess the question could be phrased, "...underestimating their chances in the late game". The casual observer sees exactly what has been mentioned here, honorable, boring, miserable. I was curious to know if these human aspects were naively dominating the raw availability of options. But its clear i was confusing brute force options with real life eventualities. Stack exchange strikes again! Thanks all! – I dont know thanks for reading Feb 12 '22 at 20:40